Rate of penetration optimization technique

ABSTRACT

A method for optimizing drilling performance is disclosed. The method includes determining, while advancing a drill bit during a drilling operation based on drilling parameters specified by a user, a rate of penetration (ROP), acquiring, using sensors disposed on drilling equipment of a well, measurement data of each drilling equipment that represents a condition of a corresponding drilling equipment at a particular ROP during the drilling operation, determining, using an artificial intelligence method based on the measurement data, a non-linear relationship between the ROP, the drilling parameters, and the conditions of the drilling equipment, identifying a constraint specified by the user based on the conditions of the drilling equipment, determining, based on the non-linear relationship and the user specified constraint, a target value of the drilling parameters to optimize a pre-determined performance measure of the drilling operation, and further performing the drilling operation based on the target value.

BACKGROUND

In drilling operations, the speed at which a drilling bit breaks the rock to lengthen the wellbore is called the rate of penetration (ROP). ROP is expressed in unit length per unit time (e.g., foot per hour) and is a critical measure to quantify the drilling performance. Consequently, a high ROP indicates fast drilling operation and, as a result, reduced cost. ROP optimization depends on multiple parameters: static (e.g., developmental field, type of formation lithology, hole size, drilling bit design, bottom-hole assembly, drilling mud type) and dynamic (e.g., weight-on-bit (WOB), rotary speed (RPM), pump flow rate, torque, standpipe pressure, and mud rheological and gravitational properties). Aside from the engineering design and choices prior to initiating the drilling operation, drillers are traditionally in charge of manually adjusting the controllable parameters based on human recommendations with the goal of achieving the highest ROP possible. For example, the Drill-Off Test (DOT) procedure is a manual time consuming process where the driller physically tests many predefined RPM (revolutions per minute) and WOB combinations in drilling and observes corresponding ROP values to select a combination that results in the highest ROP. In particular, the WOB is the amount of downward force exerted on the drill bit and is normally measured in thousands of pounds. Weight-on-bit is provided by gravity acting on the large mass of the drill collars to provide the downward force needed for the bit to efficiently break the underlying rocks.

The drilling operation is a multidimensional process with many complex surface and downhole equipment to be observed and maintained. If focus was shed on the maximization of instantaneous ROP, then drilling equipment failure is likely, which results in hazardous events and often mandates the stopping of drilling operations; hence, non-productive time (NPT) is incurred. Therefore, the maximization of the average ROP is not necessarily equivalent to the optimization of the instantaneous ROP. Rather, it is equivalent to the maximization of the instantaneous ROP and minimization of NPT. In other words, the goal should be maximizing the instantaneous ROP while not incurring any additional NPT.

Blackbox optimization (BBO) is an optimization method where the objective function is a non-differentiable blackbox function, which is a mathematical function with no analytic description of the input/output relationship, but given an arbitrary input the blackbox function returns a pre-determined function value. In other words, the blackbox function is or includes an empirical function with no analytical input/output relationship.

In mathematics, the derivative of a function is sensitivity to change of the output value of the function value with respect to a change in the input value to the function. However, when an objective function not differentiable, derivative-based methods are often slow and tend to underperform due to their inability to cope with multiple optima. Conversely, derivative-free optimization (DFO) is an optimization method that does not use derivatives and can cope more efficiently with the vast solution space and multiple optima. In DFO, information regarding the derivative of the objective function is unavailable, unreliable or impractical to obtain. For example, the objective function may be non-smooth, or time-consuming to evaluate, or in some way noisy, so that methods that rely on derivatives or approximate derivatives via finite differences are of little use.

SUMMARY

In general, in one aspect, the invention relates to a method for optimizing drilling performance of a drilling operation. The method includes determining, while advancing a drill bit during the drilling operation based on a plurality of drilling parameters specified by a user, a rate of penetration (ROP), acquiring, using a plurality of sensors disposed on a plurality of drilling equipment of a well, measurement data of each drilling equipment, wherein each measurement data represents a condition of a corresponding drilling equipment at a particular ROP during the drilling operation, determining, using an artificial intelligence method based on at least the measurement data of the plurality of drilling equipment, a non-linear relationship between the ROP, the plurality of drilling parameters, and the conditions of the plurality of drilling equipment, identifying a constraint specified by the user based at least on the conditions of the plurality of drilling equipment, determining, based at least on the non-linear relationship and the user specified constraint, a target value of the plurality of drilling parameters to optimize a pre-determined performance measure of the drilling operation, and further performing the drilling operation based on the target value of the plurality of drilling parameters.

In general, in one aspect, the invention relates to a data gathering and analysis system for optimizing drilling performance of a drilling operation. The data gathering and analysis system includes a processor and a memory coupled to the processor and storing instruction. The instructions, when executed by the processor, include functionality for determining, while advancing a drill bit during the drilling operation based on a plurality of drilling parameters specified by a user, a rate of penetration (ROP), acquiring, using a plurality of sensors disposed on a plurality of drilling equipment of a well, measurement data of each drilling equipment, wherein each measurement data represents a condition of a corresponding drilling equipment at a particular ROP during the drilling operation, determining, using an artificial intelligence method based on at least the measurement data of the plurality of drilling equipment, a non-linear relationship between the ROP, the plurality of drilling parameters, and the conditions of the plurality of drilling equipment, identifying a constraint specified by the user based at least on the conditions of the plurality of drilling equipment, determining, based at least on the non-linear relationship and the user specified constraint, a target value of the plurality of drilling parameters to optimize a pre-determined performance measure of the drilling operation, and further performing the drilling operation based on the target value of the plurality of drilling parameters.

data gathering and analysis system wellsite for performing a drilling operation of a well. The wellsite includes a rig having a plurality of drilling equipment of the well installed with a plurality of sensors, and a data gathering and analysis system including functionality for determining, while advancing a drill bit during the drilling operation based on a plurality of drilling parameters specified by a user, a rate of penetration (ROP), acquiring, using the plurality of sensors, measurement data of each drilling equipment, wherein each measurement data represents a condition of a corresponding drilling equipment at a particular ROP during the drilling operation, determining, using an artificial intelligence method based on at least the measurement data of the plurality of drilling equipment, a non-linear relationship between the ROP, the plurality of drilling parameters, and the conditions of the plurality of drilling equipment, identifying a constraint specified by the user based at least on the conditions of the plurality of drilling equipment, determining, based at least on the non-linear relationship and the user specified constraint, a target value of the plurality of drilling parameters to optimize a pre-determined performance measure of the drilling operation, and further performing the drilling operation based on the target value of the plurality of drilling parameters.

Other aspects and advantages will be apparent from the following description and the appended claims.

BRIEF DESCRIPTION OF DRAWINGS

Specific embodiments of the disclosed technology will now be described in detail with reference to the accompanying figures. Like elements in the various figures are denoted by like reference numerals for consistency.

FIGS. 1A, 1B, and 2 show a system in accordance with one or more embodiments.

FIG. 3 shows a flowchart in accordance with one or more embodiments.

FIGS. 4A, 4B, and 4C show an example in accordance with one or more embodiments.

FIG. 5 show a computing system in accordance with one or more embodiments.

DETAILED DESCRIPTION

In the following detailed description of embodiments of the disclosure, numerous specific details are set forth in order to provide a more thorough understanding of the disclosure. However, it will be apparent to one of ordinary skill in the art that the disclosure may be practiced without these specific details. In other instances, well-known features have not been described in detail to avoid unnecessarily complicating the description.

Throughout the application, ordinal numbers (e.g., first, second, third, etc.) may be used as an adjective for an element (i.e., any noun in the application). The use of ordinal numbers is not to imply or create any particular ordering of the elements nor to limit any element to being only a single element unless expressly disclosed, such as using the terms “before”, “after”, “single”, and other such terminology. Rather, the use of ordinal numbers is to distinguish between the elements. By way of an example, a first element is distinct from a second element, and the first element may encompass more than one element and succeed (or precede) the second element in an ordering of elements.

Embodiments of the invention provide a method and a system that use an ROP optimization technique (ROPOT) based on constrained blackbox (derivative-free) optimization. This real-time algorithm provides an adaptive setup to accommodate a large number of controllable drilling parameters as defined by the user to maximize the instantaneous ROP and minimize surface and downhole equipment failure instances, i.e., minimize potential non-productive time (NPT). Hence, the average ROP may be optimized for any given drilling operation and under any circumstances.

FIGS. 1A-1B show schematic diagrams of a well environment in accordance with one or more embodiments. In one or more embodiments, one or more of the modules and/or elements shown in FIGS. 1A-1B may be omitted, repeated, and/or substituted. Accordingly, embodiments disclosed herein should not be considered limited to the specific arrangements of modules and/or elements shown in FIGS. 1A-1B.

As shown in FIG. 1A, a well environment (100) includes a subterranean formation (“formation”) (104) and a well system (106). The formation (104) may include a porous or fractured rock formation that resides underground, beneath the earth's surface (“surface”) (108). The formation (104) may include different layers of rock having varying characteristics, such as varying degrees of permeability, porosity, capillary pressure, and resistivity. In the case of the well system (106) being a hydrocarbon well, the formation (104) may include a hydrocarbon-bearing reservoir (102). In the case of the well system (106) being operated as a production well, the well system (106) may facilitate the extraction of hydrocarbons (or “production”) from the reservoir (102).

In some embodiments disclosed herein, the well system (106) includes a rig (101), a wellbore (120), a well sub-surface system (122), a data gathering and analysis system (160), and a well control system (“control system”) (126). In the context of the drilling operation, the wellbore (120) is referred to as the target well. The well control system (126) may control various operations of the well system (106), such as well production operations, well drilling operation, well completion operations, well maintenance operations, and reservoir monitoring, assessment and development operations. In some embodiments, the well control system (126) includes a computer system.

The rig (101) is the machine used to drill a borehole to form the wellbore (120). Major components of the rig (101) include the drilling fluid tanks, the drilling fluid pumps (e.g., rig mixing pumps), the derrick or mast, the draw works, the rotary table or top drive, the drill string, the power generation equipment and auxiliary equipment. Drilling fluid, also referred to as “drilling mud” or simply “mud,” is used to facilitate drilling boreholes into the earth, such as drilling oil and natural gas wells. The main functions of drilling fluids include providing hydrostatic pressure to prevent formation fluids from entering into the borehole, keeping the drill bit cool and clean during drilling, carrying out drill cuttings, and suspending the drill cuttings while drilling is paused and when the drilling assembly is brought in and out of the borehole.

The wellbore (120) includes a bored hole (i.e., borehole) that extends from the surface (108) towards a target zone of the formation (104), such as the reservoir (102). An upper end of the wellbore (120), terminating at or near the surface (108), may be referred to as the “uphole” end of the wellbore (120), and a lower end of the wellbore, terminating in the formation (104), may be referred to as the “downhole” end of the wellbore (120). The wellbore (120) may facilitate the circulation of drilling fluids during drilling operations for the wellbore (120) to extend towards the target zone of the formation (104) (e.g., the reservoir (102)), facilitate the flow of hydrocarbon production (e.g., oil and gas) from the reservoir (102) to the surface (108) during production operations, facilitate the injection of substances (e.g., water) into the hydrocarbon-bearing formation (104) or the reservoir (102) during injection operations, or facilitate the communication of monitoring devices (e.g., logging tools) lowered into the formation (104) or the reservoir (102) during monitoring operations (e.g., during in situ logging operations).

In some embodiments, the well system (106) is provided with a bottom hole assembly (BHA) (151) attached to drill string (150) to suspend into the wellbore (120) for performing the well drilling operation. The bottom hole assembly (BHA) is the lowest part of a drill string and includes the drill bit, drill collar, stabilizer, mud motor, etc. A mud motor is a drilling motor that uses hydraulic horsepower of the drilling fluid to drive the drill bit during the drilling operation.

In some embodiments, the data gathering and analysis system (160) includes hardware and/or software with functionality for facilitating operations of the well system (106), such as well production operations, well drilling operation, well completion operations, well maintenance operations, and reservoir monitoring, assessment and development operations. For example, the data gathering and analysis system (160) may store drilling data records of drilling the wellbore (120) and associated offset wells (not shown). The data gathering and analysis system (160) may analyze the drilling data records to generate recommendations to facilitate drilling the wellbore (120) with an optimized rate of penetration (ROP). In this context, the data gathering and analysis system (160) is referred to as an ROP optimization advisory system. While the data gathering and analysis system (160) is shown at a well site, embodiments are contemplated where at least a portion of the data gathering and analysis system (160) is located away from well sites. In some embodiments, the data gathering and analysis system (160) may include a computer system that is similar to the computer system (500) described below with regard to FIG. 5 and the accompanying description.

FIG. 1B shows details of the rig (101) depicted in FIG. 1A above. As shown in FIG. 1B, the rig (101) includes a driller console (131), drawworks (132), mud pumps (133), shale shakers (134), a top drive (135), the drill string (150), the wellbore (120), condition monitoring sensors (138), a rotating component device (139) for unconventional drilling operations, blowout preventer (140), a communication unit (141), and a data gathering and analysis unit (142). The condition monitoring sensors (138) include surface or subsurface sensors placed or installed on selected drilling equipment to monitor real-time conditions. For example, the condition monitoring sensors (138) may be place on the mud pumps (133), the shale shakers (134), the top drive (135), the drill string (150) (at surface or below surface), the rotating component device (139) and any other equipment of the rig (101) for drilling the wellbore (120). In some embodiments, the condition monitoring sensors (138) are grouped into multiple condition monitoring packages and placed in multiple sets of drilling equipment. Each of the condition monitoring sensors (138) is capable of acquiring parameters (i.e., measurement data) related to the condition and environment of the associated equipment during the drilling operation. For example, the parameters acquired by the condition monitoring sensors (138) may identify any unexpected behavior of respective equipment such as wear, damage or other condition that may contribute to performance loss or premature failure of the equipment. In addition, the parameters acquired by the condition monitoring sensors (138) may also indicate how the equipment is reacting to drilling parameters (e.g., weight-on-bit, RPM, flow rate, etc.) specified by the driller while attempting to optimize the ROP. In one or more embodiments, the parameters acquired by the condition monitoring sensors (138) include at least one or more of the following: equipment vibrations (axial and lateral), torque, tension, compression, drag, internal and external temperature, internal and external pressure, internal and external fluid flow speed, pipe or equipment bending, distance to the drill pipe, other equipment or a wellbore wall (i.e., measuring OD of the wellbore), acoustic measurements of the equipment and surrounding, etc.

Measurement data from installed subsurface sensors are transmitted back to the surface for analysis using telemetry systems, such as through a wired pipe or wireless (e.g., acoustic, mud pulse, electromagnetic, etc.) telemetry. Measurement data generated by surface sensors or received from subsurface sensors are both transmitted to the data gathering and analysis unit (142) via wired or wireless communication, such as Bluetooth, Wi-Fi, mobile broadband, near field communications, Global System for Mobile Communications (GSM), etc. In some embodiments, a combination of two or more communication methods may be used, e.g., Wi-Fi and cable combination; near field communication, cable, and GSM combination, etc. In addition, the condition monitoring sensors (138) may be powered by embedded batteries, by wired power connections, or by energy harvesting method such as fluid turbines, solar panels, wind turbines, etc.

To facilitate the ROP optimization, the data gathering and analysis system (160) collects measurement data from surface and subsurface sensors among all condition monitoring sensors (138). In some embodiments, the measurement data from at least some sensors are streaming constantly to the data gathering and analysis system (160). In addition to or alternatively, the measurement data from other sensors are inputted periodically to the data gathering and analysis system (160). In some embodiments, the data gathering and analysis system (160) uses artificial intelligent methods, such as machine learning and deep learning models, to determine any non-linear relationships between conditions of certain drilling equipment and the ROP. In some embodiments, at least a portion of the measurement data are sent to remote computing resources using the communication unit (141). In such embodiments, analysis of the measurement data may also be performed in the Cloud, edge/fog servers, or using remote computer servers. Accordingly, analysis results from the remote computing resources are sent back to the rig (101) with via the communication unit (141).

In some embodiments, the communication unit (141) further communicates analysis results from the data gathering and analysis system (160) to the driller console (131) used by the driller to input the drilling parameters (e.g., WOB, RPM, Flow Rate, etc.) into the well control system (126) depicted in FIG. 1A above. The analysis results may be presented by the driller console (131) to the driller using a graphical and/or audible user interface.

In some embodiments, the analysis results include drilling parameter inputs that are directly sent to automated or semi-automated drilling equipment by the communication unit (141) without action or intervention from the driller. In some other embodiments, a confirmation from the driller is required before the drilling parameter inputs from the communication unit (141) are accepted by the automated/semi-automated drilling equipment.

Turning to FIG. 2 , FIG. 2 shows a schematic diagram of the data gathering and analysis system (160) in accordance with one or more embodiments. In one or more embodiments, one or more of the modules and/or elements shown in FIG. 2 may be omitted, repeated, and/or substituted. Accordingly, embodiments of the disclosure should not be considered limited to the specific arrangements of modules and/or elements shown in FIG. 2 .

FIG. 2 illustrates the data gathering and analysis system (160) that has multiple components, including, for example, a buffer (204), a drilling modelling engine (201), a constrained optimization engine (201), and a drilling design engine (203). Each of these components (201, 202, 203, 204) may be located and executed on a same computing device (e.g., a general purpose personal computer (PC), laptop, tablet PC, smart phone, multifunction printer, kiosk, server, etc.) or on different computing devices that are connected via a network, such as a wide area network or a portion of Internet of any size having wired and/or wireless segments. Each of these components of the data gathering and analysis system (160) is discussed below.

In one or more embodiments of the invention, the buffer (204) may be implemented in hardware (i.e., circuitry), software, or any combination thereof. The buffer (204) is configured to store data generated and/or used by the data gathering and analysis system (160). The data stored in the buffer (204) includes controllable input drilling parameters (205), non-controllable sensor measurements (206), blackbox function (207), machine-learned non-linear relationship (208), and drilling parameter target values (209).

The controllable input drilling parameters (205) are user specified drilling parameters for performing a drilling operation of a well. For example, the controllable input drilling parameters (205) may include weight-on-bit, drilling rotary speed, rig pump flow rate, etc.

The non-controllable sensor measurements (206) are measurement data acquired by condition monitoring sensors disposed on various pieces of drilling equipment, such as mud pumps, shale shakers, the top drive, the drill string, the rotating component device, and any other equipment of the drilling rig. The measurement data may represent one or more of standpipe pressure, return flow rate, bit condition, hole learning index, equivalent circulating density (ECD), top-drive torque, top-drive hydraulics and electronics condition, stuck-pipe index, surface and downhole drill string vibration, bottomhole-assembly condition, drilling mud properties, hole geometry, etc.

The blackbox function (207) is an empirical function representing a relationship between the controllable input drilling parameters (205), the non-controllable sensor measurements (206), and a pre-determined drilling performance measure to be optimized for the drilling operation. For example, the drilling performance measure may correspond to rate-of-penetration (ROP), cost per foot, number of run bits, total number of trips or a combination thereof of the drilling operation.

The machine-learned non-linear relationship (208) is a non-linear mathematical relationship (e.g., a formula, a function, an algorithm, etc.) representing a non-analytical portion of the blackbox function (207).

The drilling parameter target values (209) are a set of values of the non-controllable input drilling parameters (205) that, when applied to the drilling equipment, will lead to an optimal result of the drilling performance measure.

In one or more embodiments, the drilling modelling engine (201), the constrained optimization engine (201), and the drilling design engine (203) may be implemented in hardware (i.e., circuitry), software, or any combination thereof.

In one or more embodiments, the drilling modelling engine (201) is configured to generate the blackbox function (207) by applying machine learning or deep learning algorithms to the controllable input drilling parameters (205), the non-controllable sensor measurements (206) and a measured rate-of-penetration (ROP).

In one or more embodiments, the constrained optimization engine (202) is configured to generate target values of the drilling parameters to optimize a pre-determined performance measure of the drilling operation. In particular, the constrained optimization engine (202) iteratively applies a constrained optimization algorithm to the blackbox function (207) to determine the target values of drilling parameters while meeting the user specified constraints.

In one or more embodiments, the drilling design engine (203) is configured to generate an engineering design specification of the drilling parameters and drilling equipment for a subsequent drilling operation of a new well based on the blackbox function of the current drilling operation of the current well.

In one or more embodiments, the data gathering and analysis system (160) performs the functionalities described above using the method described in reference to FIG. 3 below. Although the data gathering and analysis system (160) is shown as having three engines (201, 202, 203), in other embodiments of the invention, the data gathering and analysis system (160) may have more or fewer engines and/or more or fewer other components. Further, the functionality of each component described above may be split across components. Further still, each component (201, 202, 203) may be utilized multiple times to carry out an iterative operation.

Turning to FIG. 3 , FIG. 3 shows a flowchart in accordance with one or more embodiments. Specifically, FIG. 3 describes a method of optimizing drilling performance of a drilling operation. One or more blocks in FIG. 3 may be performed using one or more components as described in FIGS. 1A, 1B, and 2 . While the various blocks in FIG. 3 are presented and described sequentially, one of ordinary skill in the art will appreciate that some or all of the blocks may be executed in different orders, may be combined or omitted, and some or all of the blocks may be executed in parallel. Furthermore, the blocks may be performed actively or passively.

Initially in Block 300, a rate of penetration (ROP) is determined while advancing a drill bit during a drilling operation. The drilling operation is performed based on drilling parameters (e.g., weight-on-bit, rotary speed, flow rate, etc.) specified by a user (e.g., by a drilling technician via a driller console). The ROP may be determined using a downhole sensor.

In Block 302, measurement data of each drilling equipment of the drilling operation is acquired using sensors disposed on multiple pieces of drilling equipment of the well. Each measurement data represents a condition of a corresponding drilling equipment at a particular ROP during the drilling operation. For example, condition monitoring sensors may be disposed on mud pumps, shale shakers, the top drive, the drill string (at surface or below surface), the rotating component device, and any other equipment of the drilling rig. The conditions of the drilling equipment may include one or more of standpipe pressure, return flow rate, bit condition, hole cleaning index, equivalent circulating density (ECD), top-drive torque, top-drive hydraulics and electronics condition, stuck-pipe index, surface and downhole drill string vibration, bottomhole-assembly condition, drilling mud properties, and hole geometry.

In Block 304, a blackbox function is generated that describes a relationship between a performance measure of the drilling operation with respect to the drilling parameters and the conditions of the drilling equipment. For example, the performance measure may be the ROP, cost per foot, total number of trips, a combination of these, etc. The blackbox function is formulated by the controllable drilling parameters as well as artificial intelligence method(s) based on at least the sensor measurement data of the drilling equipment to model and predict the drilling equipment and operation conditions. The AI method may be any suitable machine learning (ML) or other AI algorithm such as neural network algorithms, Naive Bayes, Decision Tree, vector-based algorithms such as Support Vector Machines, or regression based algorithms such as linear regression, unsupervised ML algorithms, etc.

The blackbox function or blackbox objective function is formulated by an SME and it is solved by using a derivative free optimization solver (some are considered to be AI algorithms), such as Bayesian optimization, evolution strategies, Nelder-Mead method, simulated annealing, genetic algorithms, particle swarm optimization, ant colony optimization, among others. In one example scenario, consider the vast solution space needed to be explored to find the best ROP. One may change the flow in, WOB, RPM, etc. Finding an optimal set of values would require an infinite number combinations of these values. As this is unfeasible, derivative free optimization algorithms aim to explore the solution space in a much more efficient way while considering a set of constraints or inequalities. While these derivative-free optimization algorithms do not guarantee to find the optimal value of a function, but often produce much better results than simply random trials.

A physics-based analytical portion of the blackbox function is generated based on physics formulas, such as hydraulics formula, torque and drag formula, geomechanics formula, etc. A non-analytical portion of the blackbox includes a machine-learned non-linear relationship between the ROP, the drilling parameters, and the conditions of the drilling equipment. For example, anomaly detection (e.g., principal component analysis, clustering, 1-class models, etc.), regression (e.g., artificial neural networks, convolutional neural networks, etc.), and/or multi-class classification models (e.g., random forest, support vector machine, etc.) may be used to generate the machine-learned non-linear relationship. Accordingly, the blackbox function is used as an objective function to represent the pre-determined performance measure of the drilling operation. In one or more embodiments, use of ML or physics-based models may be used to generate more sophisticated measurements that are taken as input for the optimization algorithm. For example, an ML model for the prediction of stuck pipe index may be used.

In Block 306, a constraint is specified by the user based at least on the conditions of the drilling equipment. The constraint defines an acceptable operating range of the conditions of the drilling equipment. For example, the acceptable range may include an extreme value (e.g., maximum, minimum) of one or more of top drive torque, weight-on-bit, fluid flow rate, stick-slip index, bit wear rate, stuck pipe probability index, and cuttings concentration in annulus, among others. Taking the stuck pipe index example from above, this index may be used as part of a constraint for the derivative free optimization algorithm. For example, a constraint may be “do not increase ROP at the expense of increasing the stuck pipe index.”

In Block 308, a target value of the drilling parameters is determined to optimize the blackbox function that represents the performance measure of the drilling operation. The target value is determined based at least on the non-linear relationship and the user specified constraint. In particular, the target value of the drilling parameters is determined by applying an iterative optimization algorithm to the blackbox function while meeting the user specified constraint. In other words, the blackbox function is designated as the objection function of the constrained derivative-free optimization algorithm, which may include Bayesian optimization algorithm, evolution strategies algorithm, Nelder-Mead method, simulated annealing algorithm, genetic algorithms, particle swarm optimization algorithm, ant colony optimization algorithm, among others.

In Block 310, the drilling operation is further performed based on the target value of the drilling parameters. As the drill bit advances during the drilling operation, the blackbox function is continuously updated based on real time condition monitoring sensor measurement data. Accordingly, the target value of the drilling parameters evolves in real time to optimize the drilling operation.

In Block 312, the drilling parameters of a subsequent drilling operation is specified based on the blackbox function. While the blackbox function is based on real time condition monitoring sensor measurement data acquired during the current drilling operation of the current well, the blackbox function is used as a surrogate or proxy for the subsequent drilling operation of a new well in the same geographical region as the current well. For example, the drilling parameters and drilling equipment may be specified in the engineering design of the subsequent drilling operation based on the blackbox function of the current drilling operation of the current well.

Turning to FIGS. 4A-4C, FIGS. 4A-4C provide an example of the ROP optimization technique. The example shown in FIGS. 4A-4C may be, for example, based on one or more components depicted in FIGS. 1A-1B and 2 , and the method flowchart depicted in FIG. 3 above. In one or more embodiments, one or more of the modules and/or elements shown in FIGS. 4A-4C may be omitted, repeated, and/or substituted. Accordingly, embodiments disclosed herein should not be considered limited to the specific arrangements of modules and/or elements shown in FIGS. 4A-4C.

FIG. 4A shows a general workflow of the ROP optimization technique (ROPOT). As shown in FIG. 4A, the input data (401) encompasses any observable parameter or measurable quantity that are associated with the drilling operation, both on surface and downhole. Examples include equipment parameters (401 a) (e.g., weight-on-bit, drilling rotary speed, rig pump flow rate, etc.) and measurements (401 b) (e.g., standpipe pressure, return flow rate, bit condition, hole learning index, equivalent circulating density (ECD), top-drive torque, top-drive hydraulics and electronics condition, stuck-pipe index, surface and downhole drill string vibration, bottomhole-assembly condition, drilling mud properties, hole geometry, etc.). Any and all equipment relevant to the drilling operation may be included. The equipment may have built-in sensors or were selectively upgraded with sensors to monitor their conditions. These readings are used as inputs to the ROP optimization algorithm (402).

The ROP optimization algorithm (402) includes physics-based (e.g., hydraulics, torque and drag, geomechanics, etc.) and machine learning algorithms (402 b) that are used to model and predict the drilling equipment and operation conditions to capture aspects where sensors are missing or infeasible. The machine learning portion of the algorithms (402 b) is used to generate empirical relationship(s), in addition to the physics-based analytical relationship(s), between various aspects of the input data (401) and the ROP. An objective function is generated based on the empirical relationship(s) as well as the physics-based analytical relationship(s) to represent a performance measure (e.g., ROP) of the drilling operation. Because the non-analytical aspect of the empirical relationship(s), the objective function is a blackbox function. For example, the objective function may represent the empirical relationship between ROP and the input data (401) with no analytical input/output relationship. As the drill bit advances during the drilling operation, the input data (401) are collected in real time for the physics-based and machine learning algorithms (402 b) to continuously generate and adjust the objective function.

The equipment parameters (401 a), measurements (401 b), and modelling results (i.e., objective function) from the physics-based and machine learning algorithms (402 b) are then fed to a real-time optimizer (402 a) which generates, in real time and in an iterative fashion (detailed below), the recommended optimal combination of controllable input parameters (403 a), which are target values of the equipment parameters (401 a) that achieve an optimal output of the objective function. The optimization solution is constrained by the measurements (401 b) and predictions obtained from the physics-based and machine learning algorithms (402 b) to prevent equipment failure or undesired drilling conditions (403 b), hence minimize NPT, while searching for optimal controllable parameters (403 a) to maximize ROP. In addition to improving the drilling process operationally, the ROPOT may also be used to optimize the well drilling engineering design by using surrogate-based optimization which returns a data-driven proxy for ROP and NPT prediction to be used in optimizing the drilling engineering design of a new well.

The constrained optimization solution generated by the optimizer (402 a) is mathematically represented as

${\max\limits_{x}{f\left( {x,y} \right)}{subject}{to}}\begin{matrix} {{{g_{i}\left( {x,y} \right)} \leq {C_{g_{i}}\left( {x,y} \right)}},} & {{i = 1},\ldots,m} \\ {{{h_{j}\left( {x,y} \right)} = {C_{h_{j}}\left( {x,y} \right)}},} & {{j = 1},\ldots,p} \end{matrix}$

-   -   x ∈         ^(n): n-dimensional vector of the controllable input drilling         parameters, n ∈     -   y ∈         ^(l): l-dimensional vector of the non-controllable sensor         measurements, e.g., static data, components specifications,         etc., l ∈     -   f(x, y) ∈         : objective function to be optimized     -   g_(i)(x, y)≤C_(g) _(i) (x, y): inequality constraints, where         g_(i)(x, y) ∈         is a sensor measurement, a physics-based or machine learning         algorithm that evaluates the state of a drilling aspect (e.g.,         hole cleaning, vibrations, etc.) while C_(g) _(i) (x, y) ∈         describes the corresponding inequality constraint     -   h_(j)(x, y)=C_(h) _(j) (x, y): equality constraints, where         h_(j)(x) ∈         is a sensor measurement, a physics-based or machine learning         algorithm that evaluates the state of a drilling aspect (e.g.,         hole cleaning, vibrations, etc.) C_(h) _(j) (x, t) ∈         describes the corresponding equality constraint     -   m ∈         : number of inequality constraints     -   p ∈         : number of equality constraints     -   Where         and         represent real and natural numbers, respectively.

The objective function f(x, y) may be formulated as ROP, cost per foot, total number of trips, and/or a combination of these objective functions, among others. However, the functional form of f(x, y) with respect to the drilling parameters (401 a) (i.e., x_(k)) and measurements (401 b) (i.e., y_(k)) is unknown and impractical to obtain. Therefore, the constrained optimization solution is to be solved by the optimizer (402 a) using a blackbox (BBO) or derivative-free optimization (DFO) method.

FIG. 4B shows the optimization workflow as an iterative process where the optimization algorithm (solver) (411) aims to find the optimal combination (411 b) of input variables (411 a), referred to as x_(opt) that collectively result in an optimal output of the optimized object (412). Note that weight-on-bit, rotary speed, and pump flow rate are abbreviated as WOB, RPM, and GPM, respectively. The input variables (411 a) and the optimization algorithm (411) correspond to the input data (401) and the optimizer (402 a), respectively, depicted in FIG. 4A above. The optimized object (412) and the optimal combination (411 b) correspond to the objective function generated by the drilling modelling (402 b) and the target equipment parameter values to optimize the objective function, as described in reference to FIG. 4A above.

The optimization algorithm (411) starts with an initial guess or seed, x₀, which may be based on the optimal drilling parameter vector inferred from offset wells. The optimization algorithm (411) performs multiple iterations (413), where each iteration k involves a proposed sample drilling parameter vector x_(k) that is evaluated by the blackbox function (412) along with sensor measurement vector y_(k) to compute the objective function f(x_(k), y_(k)), the constrained quantities (g(x_(k), y_(k)) and h(x_(k), y_(k))), and the constraints (C_(g) _(k) (x_(k), y_(k)) and C_(h) _(k) (x_(k), y_(k)) at this sample point. In drilling terminology, this corresponds to an autonomous and physically constrained drill-off test (DFT) that aims to optimize the average ROP. Throughout multiple iterations (413), ∇f(x, y), ∇²f(x, y), and/or other mathematical derivatives are not explicitly accessible because the optimized object (412) is a blackbox function. Therefore, the optimization algorithms (411) are based on algorithms that converges fast without getting stuck in local optima (i.e., suboptimal combination of dynamic drilling parameters). Examples of optimization algorithms (411) include Bayesian optimization, evolution strategies, Nelder-Mead method, simulated annealing, genetic algorithms, particle swarm optimization, ant colony optimization, among others.

In addition to using the optimization workflow to determine optimized ROP during the drilling operation, the optimization workflow shown in FIG. 4B may be reformulated to facilitate engineering design activities where it is difficult to predict the time required to drill a section optimally, therefore design choices of drilling equipment for a given well are uncertain. FIG. 4C illustrate the ROPOT workflow that is adjusted to be a surrogate-based optimization technique to serve as an improved formulation to both operation and engineering applications. The surrogate-based ROPOT starts in block 421 where initial samples (i.e., controllable input drilling parameters x) are acquired from the design space, then in block 422 the initial samples are evaluated operationally (experimentally) on the rig (similar settings to drill-off tests). In other words, a range of initial controllable input drilling parameters are applied to corresponding automated or semi-automated drilling equipment when ROP is continuously observed and recorded as a training data set for machine learning or deep learning modelling. For this, anomaly detection (e.g., principal component analysis, clustering, 1-class models, etc.), regression (e.g., artificial neural networks, convolutional neural networks, etc.), or multi-class classification models (e.g., random forest, support vector machine, etc.) may be used to map the controllable drilling parameters with the ROP, also referred to as reinforced sampling. Next in block 423, further sampling is conducted using sampling algorithms (e.g., random, space-filling, adaptive) to capture the more nonlinear regions of the design space. In other words, additional controllable input drilling parameters x are identified by random, space-filling, and/or adaptive means from the range of initial controllable input drilling parameters to augment the training data set for machine/deep learning (ML/DL) described above. To assess the quality of the generated data and to improve the selection of data during the sampling process, the training of the models (mapping drilling parameters to ROP) is repeated in an iteration loop (423 a) until a defined loss function (423 b) exceeds a given set of criteria (423 c). Different loss functions may be used to assess these data depending on the category of ML/DL models used during the reinforced sampling, e.g., absolute error or smooth absolute error for regression models and binary cross entropy, margin classifier, among others, for multi class classification models. In block 424, the machine learning or deep learning model (424 a) is trained to yield a surrogate or proxy that maps the function f(x, y) from the current drilling operation of the current well to a future drilling operation of a new well and also capture any other functions, such as casing design, trajectory optimization, among others. as desired by the engineering team). Operationally in block 425, an optimizer (425 a) is used to find the optimal point of this surrogate or proxy. Subsequent engineering designs can then use this surrogate to design future drilling jobs in the same geographical area.

The ROPOT workflow depicted in FIG. 4C may be referred to as an optimization session, which may be run/re-run by drilling operation users or engineering users (e.g., driller, foreman, etc.) whenever the ROP needs to be optimized or re-optimized. Example scenarios of where a new optimization session is needed include the beginning of drilling a new hole section, entering a new formation, detecting any degraded ROP performance, NPT incident (e.g., kick, lost circulation, etc.), etc.

Three example ROPOT implementation scenarios (a), (b), and (c) are illustrated below. These examples emphasize the concept that ROPOT is flexible and adaptable to a vast variety of drilling operations and equipment. Note that these examples may be considered analogously for the surrogate-based ROPOT implementation. In each example, details about a given drilling operation sufficient to demonstrate the implementation of ROPOT are described while details of physics-based and machine learning models are omitted. Note that the objective function in all examples is the same f=f(x, y). Inequality and equality constraints are denoted as g=g(x, y) and h=h(x, y), respectively. Note that constraint limits and thresholds are only examples for demonstration and do not reflect any actual drilling data.

(a) Basic Vertical Drilling Operation

-   -   Description: In this operation, a typical rig drilling of a 8-⅜         inch vertical hole section with a simple bottom hole assembly.         Drilling ROP needs to be optimized.     -   Input Parameters: three input parameters (n=3) in this example,         which are weight-on-bit (WOB), rotary speed (RPM), and pump flow         rate (GPM), i.e., x=(WOB, RPM, GPM)     -   Constraints: four inequality constraints (m=4 and p=0).         -   Maximum top drive torque:         -   g₁=topdrive torque sensor measurement and C₁=15             kilopounds-foot         -   Maximum WOB allowed:         -   g₂=WOB loadcell sensor measurement and C₂=60 kilopounds         -   Maximum GPM allowed:         -   g₃=GPM from Pump counter and C₃=500 gallons per minute         -   Minimum GPM allowed:         -   g₄=g₃=GPM from Pump counter and C₄=−300 gallons per minute     -   Optimal Parameters: x_(opt)=(WOB_(opt), RPM_(opt), GPM_(opt))

(b) Basic Horizontal Drilling Operation

-   -   Description: In this operation, a typical rig drilling of a 5-⅞         inch horizontal hole section with a bottom hole assembly         including measurement while drilling (MWD), logging while         drilling (LWD), and rotary steerable system (RSS). Drilling ROP         needs to be optimized.     -   Input Parameters: three input parameters (n=3), i.e., x=(WOB,         RPM, GPM)     -   Constraints: seven inequality constraints (m=7 and p=1).         -   Maximum top drive torque:         -   g₁=topdrive torque sensor measurement and C₁=20             kilopounds-foot         -   Maximum WOB allowed:         -   g₂=WOB loadcell sensor measurement and C₂=50 kilopounds         -   Maximum GPM allowed:         -   g₃=GPM from Pump counter and C₃=350 gallons per minute         -   Minimum GPM allowed:         -   g₄=g₃=GPM from Pump counter and C₄=−200 gallons per minute         -   Stick-slip index (SSI) threshold:         -   g₅=SSI from MWD and C₅=40%         -   Stuck pipe probability index based on a pretrained machine             learning model:         -   g₆=stuckpipe probability index and C₆=50%         -   Bit wear rate as computed using a physics-based,             data-driven, or hybrid model:         -   g₇=Bit wear rate and C₇=10%         -   Maintain a stable equivalent circulating density (ECD) to             avoid induced fractures or influxes         -   h₁=ECD and C₈=11 ppg     -   Optimal Parameters: x_(opt)=(WOB_(opt), RPM_(opt), GPM_(opt))         (c) Basic Horizontal Drilling Operation without Subsurface Data     -   Description: In this operation, a typical rig drilling of a 5-⅞         inch horizontal hole section with a simple bottom hole that does         not include subsurface tools (i.e., LWD, MWD, etc.). Drilling         cost per foot needs to be optimized while ensuring proper hole         cleaning. One formula to compute cost per foot is:

$\frac{\$}{ft} = \frac{{{Bit}{Cost}} + {{Rig}{Daily}{Rate} \times \left( {{{Drilling}{time}} + {{Tripping}{Time}}} \right)}}{{Footage}{Drilled}}$

-   -   Input Parameters: three input parameters (n=3), i.e. x=(WOB,         RPM, GPM)     -   Constraints: seven inequality constraints (m=7 and p=0).         -   Maximum top drive torque:         -   g₁=topdrive torque sensor measurement and C₁=20             kilopounds-foot         -   Maximum WOB allowed:         -   g₂=WOB loadcell sensor measurement and C₂=50 kilopounds         -   Maximum GPM allowed:         -   g₃=GPM from Pump counter and C₃=350 gallons per minute         -   Minimum GPM allowed:         -   g₄=g₃=GPM from Pump counter and C₄=−200 gallons per minute         -   Stuck pipe probability index based on a pretrained machine             learning model:         -   g₅=stuckpipe probability index and C₅=50%         -   Bit wear rate as computed using a physics-based,             data-driven, or hybrid model:         -   g₆=Bit wear rate and C₆=10%         -   Maximum Cuttings Concentration in Annulus (CCA) allowed:         -   g₇=CCA calculated from equation Eq. 1 and C₇=5%

$\begin{matrix} {{{CCA} = \frac{{ROP} \times {Hole}{size}^{2}}{1471{GPM} \times \left\lbrack \left( {1 - {{Vs}/{Vft}}} \right) \right\rbrack \times 100}},} & \left. {{Eq}.1} \right) \end{matrix}$

-   -   -   Where Vs and Vft refer to the cutting slip velocity (ft/min)

    -   Optimal Parameters: x_(opt)=(WOB_(opt), RPM_(opt), GPM_(opt))

Embodiments of the invention have the following advantages: (1) improving optimization results of ROP, cost-per-foot, number of run bits, etc. by utilizing derivative-free optimization algorithms (genetic algorithms, simulated annealing, etc.), (2) using drilling models that do not rely on historical offset data, i.e., do not use a supervised learning algorithms, (3) independently optimizing each new drilling session (e.g., start of a new section, resume drilling operations after NPT, etc.), and (4) including and accounting for the operational constraints and inputs from physics-based (ECD, CCA, etc.) and machine learning models (stuck pipe index, lost circulation, etc.).

Embodiments may be implemented on a computer system. FIG. 5 is a block diagram of a computer system (500) used to provide computational functionalities associated with described algorithms, methods, functions, processes, flows, and procedures as described in the instant disclosure, according to an implementation. The illustrated computer (500) is intended to encompass any computing device such as a high performance computing (HPC) device, a server, desktop computer, laptop/notebook computer, wireless data port, smart phone, personal data assistant (PDA), tablet computing device, one or more processors within these devices, or any other suitable processing device, including both physical or virtual instances (or both) of the computing device. Additionally, the computer (500) may include a computer that includes an input device, such as a keypad, keyboard, touch screen, or other device that can accept user information, and an output device that conveys information associated with the operation of the computer (500), including digital data, visual, or audio information (or a combination of information), or a GUI.

The computer (500) can serve in a role as a client, network component, a server, a database or other persistency, or any other component (or a combination of roles) of a computer system for performing the subject matter described in the instant disclosure. The illustrated computer (500) is communicably coupled with a network (530). In some implementations, one or more components of the computer (500) may be configured to operate within environments, including cloud-computing-based, local, global, or other environment (or a combination of environments).

At a high level, the computer (500) is an electronic computing device operable to receive, transmit, process, store, or manage data and information associated with the described subject matter. According to some implementations, the computer (500) may also include or be communicably coupled with an application server, e-mail server, web server, caching server, streaming data server, business intelligence (BI) server, or other server (or a combination of servers).

The computer (500) can receive requests over network (530) from a client application (for example, executing on another computer (500)) and responding to the received requests by processing the said requests in an appropriate software application. In addition, requests may also be sent to the computer (500) from internal users (for example, from a command console or by other appropriate access method), external or third-parties, other automated applications, as well as any other appropriate entities, individuals, systems, or computers.

Each of the components of the computer (500) can communicate using a system bus (503). In some implementations, any or all of the components of the computer (500), both hardware or software (or a combination of hardware and software), may interface with each other or the interface (504) (or a combination of both) over the system bus (503) using an application programming interface (API) (512) or a service layer (513) (or a combination of the API (512) and service layer (513). The API (512) may include specifications for routines, data structures, and object classes. The API (512) may be either computer-language independent or dependent and refer to a complete interface, a single function, or even a set of APIs. The service layer (513) provides software services to the computer (500) or other components (whether or not illustrated) that are communicably coupled to the computer (500). The functionality of the computer (500) may be accessible for all service consumers using this service layer. Software services, such as those provided by the service layer (513), provide reusable, defined business functionalities through a defined interface. For example, the interface may be software written in JAVA, C++, or other suitable language providing data in extensible markup language (XML) format or other suitable format. While illustrated as an integrated component of the computer (500), alternative implementations may illustrate the API (512) or the service layer (513) as stand-alone components in relation to other components of the computer (500) or other components (whether or not illustrated) that are communicably coupled to the computer (500). Moreover, any or all parts of the API (512) or the service layer (513) may be implemented as child or sub-modules of another software module, enterprise application, or hardware module without departing from the scope of this disclosure.

The computer (500) includes an interface (504). Although illustrated as a single interface (504) in FIG. 5 , two or more interfaces (504) may be used according to particular needs, desires, or particular implementations of the computer (500). The interface (504) is used by the computer (500) for communicating with other systems in a distributed environment that are connected to the network (530). Generally, the interface (504) includes logic encoded in software or hardware (or a combination of software and hardware) and operable to communicate with the network (530). More specifically, the interface (504) may include software supporting one or more communication protocols associated with communications such that the network (530) or interface's hardware is operable to communicate physical signals within and outside of the illustrated computer (500).

The computer (500) includes at least one computer processor (505). Although illustrated as a single computer processor (505) in FIG. 5 , two or more processors may be used according to particular needs, desires, or particular implementations of the computer (500). Generally, the computer processor (505) executes instructions and manipulates data to perform the operations of the computer (500) and any algorithms, methods, functions, processes, flows, and procedures as described in the instant disclosure.

The computer (500) also includes a memory (506) that holds data for the computer (500) or other components (or a combination of both) that may be connected to the network (530). For example, memory (506) may be a database storing data consistent with this disclosure. Although illustrated as a single memory (506) in FIG. 5 , two or more memories may be used according to particular needs, desires, or particular implementations of the computer (500) and the described functionality. While memory (506) is illustrated as an integral component of the computer (500), in alternative implementations, memory (506) may be external to the computer (500).

The application (507) is an algorithmic software engine providing functionality according to particular needs, desires, or particular implementations of the computer (500), particularly with respect to functionality described in this disclosure. For example, application (507) can serve as one or more components, modules, applications, etc. Further, although illustrated as a single application (507), the application (507) may be implemented as multiple applications (507) on the computer (500). In addition, although illustrated as integral to the computer (500), in alternative implementations, the application (507) may be external to the computer (500).

There may be any number of computers (500) associated with, or external to, a computer system containing computer (500), each computer (500) communicating over network (530). Further, the term “client,” “user,” and other appropriate terminology may be used interchangeably as appropriate without departing from the scope of this disclosure. Moreover, this disclosure contemplates that many users may use one computer (500), or that one user may use multiple computers (500).

In some embodiments, the computer (500) is implemented as part of a cloud computing system. For example, a cloud computing system may include one or more remote servers along with various other cloud components, such as cloud storage units and edge servers. In particular, a cloud computing system may perform one or more computing operations without direct active management by a user device or local computer system. As such, a cloud computing system may have different functions distributed over multiple locations from a central server, which may be performed using one or more Internet connections. More specifically, cloud computing system may operate according to one or more service models, such as infrastructure as a service (IaaS), platform as a service (PaaS), software as a service (SaaS), mobile “backend” as a service (MBaaS), serverless computing, artificial intelligence (AI) as a service (AIaaS), and/or function as a service (FaaS).

While the disclosure has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this disclosure, will appreciate that other embodiments may be devised which do not depart from the scope of the disclosure as disclosed herein. Accordingly, the scope of the disclosure should be limited only by the attached claims. 

What is claimed is:
 1. A method for optimizing drilling performance of a drilling operation, the method comprising: determining, while advancing a drill bit during the drilling operation based on a plurality of drilling parameters specified by a user, a rate of penetration (ROP); acquiring, using a plurality of sensors disposed on a plurality of drilling equipment of a well, measurement data of each drilling equipment, wherein each measurement data represents a condition of a corresponding drilling equipment at a particular ROP during the drilling operation; determining, using an artificial intelligence method based on at least the measurement data of the plurality of drilling equipment, a non-linear relationship between the ROP, the plurality of drilling parameters, and the conditions of the plurality of drilling equipment; identifying a constraint specified by the user based at least on the conditions of the plurality of drilling equipment; determining, based at least on the non-linear relationship and the user specified constraint, a target value of the plurality of drilling parameters to optimize a pre-determined performance measure of the drilling operation; and further performing the drilling operation based on the target value of the plurality of drilling parameters.
 2. The method according to claim 1, further comprising: generating, using the artificial intelligence method based on at least the measurement data of the plurality of drilling equipment, a blackbox function that describes a relationship between a performance measure of the drilling operation with respect to the plurality of drilling parameters and the conditions of the plurality of drilling equipment, wherein the blackbox function is used as an objective function to represent the pre-determined performance measure of the drilling operation, and wherein the target value of the plurality of drilling parameters is determined by applying an iterative optimization algorithm to the objective function while meeting the user specified constraint.
 3. The method according to claim 2, wherein the blackbox function comprises the non-linear relationship and at least one physics-based analytical relationship.
 4. The method according to claim 3, further comprising: specifying, based on the blackbox function, the plurality of drilling parameters of a subsequent drilling operation.
 5. The method according to claim 1, wherein the plurality of drilling parameters comprise a weight-on-bit value, a rotary speed value, and a pump flow rate value.
 6. The method according to claim 1, wherein the conditions of the plurality of drilling equipment comprise standpipe pressure, return flow rate, bit condition, hole learning index, equivalent circulating density (ECD), top-drive torque, top-drive hydraulics and electronics condition, stuck-pipe index, surface and downhole drill string vibration, bottomhole-assembly condition, drilling mud properties, and hole geometry.
 7. The method according to claim 1, wherein the constraint defines an acceptable operating range of the conditions of the plurality of drilling equipment, and wherein the acceptable range comprises an extreme value of one or more of top drive torque, weight-on-bit, fluid flow rate, stick-slip index, bit wear rate, stuck pipe probability index, and cuttings concentration in annulus.
 8. A data gathering and analysis system for optimizing drilling performance of a drilling operation, comprising: a processor; and a memory coupled to the processor and storing instruction, the instructions, when executed by the processor, comprising functionality for: determining, while advancing a drill bit during the drilling operation based on a plurality of drilling parameters specified by a user, a rate of penetration (ROP); acquiring, using a plurality of sensors disposed on a plurality of drilling equipment of a well, measurement data of each drilling equipment, wherein each measurement data represents a condition of a corresponding drilling equipment at a particular ROP during the drilling operation; determining, using an artificial intelligence method based on at least the measurement data of the plurality of drilling equipment, a non-linear relationship between the ROP, the plurality of drilling parameters, and the conditions of the plurality of drilling equipment; identifying a constraint specified by the user based at least on the conditions of the plurality of drilling equipment; determining, based at least on the non-linear relationship and the user specified constraint, a target value of the plurality of drilling parameters to optimize a pre-determined performance measure of the drilling operation; and further performing the drilling operation based on the target value of the plurality of drilling parameters.
 9. The data gathering and analysis system according to claim 8, the instructions, when executed by the processor, further comprising functionality for: generating, using the artificial intelligence method based on at least the measurement data of the plurality of drilling equipment, a blackbox function that describes a relationship between a performance measure of the drilling operation with respect to the plurality of drilling parameters and the conditions of the plurality of drilling equipment, wherein the blackbox function is used as an objective function to represent the pre-determined performance measure of the drilling operation, and wherein the target value of the plurality of drilling parameters is determined by applying an iterative optimization algorithm to the objective function while meeting the user specified constraint.
 10. The data gathering and analysis system according to claim 9, wherein the blackbox function comprises the non-linear relationship and at least one physics-based analytical relationship.
 11. The data gathering and analysis system according to claim 10, the instructions, when executed by the processor, further comprising functionality for: specifying, based on the blackbox function, the plurality of drilling parameters of a subsequent drilling operation.
 12. The data gathering and analysis system according to claim 8, wherein the plurality of drilling parameters comprise a weight-on-bit value, a rotary speed value, and a pump flow rate value.
 13. The data gathering and analysis system according to claim 8, wherein the conditions of the plurality of drilling equipment comprise standpipe pressure, return flow rate, bit condition, hole learning index, equivalent circulating density (ECD), top-drive torque, top-drive hydraulics and electronics condition, stuck-pipe index, surface and downhole drill string vibration, bottomhole-assembly condition, drilling mud properties, and hole geometry.
 14. The data gathering and analysis system according to claim 8, wherein the constraint defines an acceptable operating range of the conditions of the plurality of drilling equipment, and wherein the acceptable range comprises an extreme value of one or more of top drive torque, weight-on-bit, fluid flow rate, stick-slip index, bit wear rate, stuck pipe probability index, and cuttings concentration in annulus.
 15. A wellsite for performing a drilling operation of a well, comprising: a rig having a plurality of drilling equipment of the well installed with a plurality of sensors; and a data gathering and analysis system comprising functionality for: determining, while advancing a drill bit during the drilling operation based on a plurality of drilling parameters specified by a user, a rate of penetration (ROP); acquiring, using the plurality of sensors, measurement data of each drilling equipment, wherein each measurement data represents a condition of a corresponding drilling equipment at a particular ROP during the drilling operation; determining, using an artificial intelligence method based on at least the measurement data of the plurality of drilling equipment, a non-linear relationship between the ROP, the plurality of drilling parameters, and the conditions of the plurality of drilling equipment; identifying a constraint specified by the user based at least on the conditions of the plurality of drilling equipment; determining, based at least on the non-linear relationship and the user specified constraint, a target value of the plurality of drilling parameters to optimize a pre-determined performance measure of the drilling operation; and further performing the drilling operation based on the target value of the plurality of drilling parameters.
 16. The wellsite according to claim 15, the data gathering and analysis system further comprising functionality for: generating, using the artificial intelligence method based on at least the measurement data of the plurality of drilling equipment, a blackbox function that describes a relationship between a performance measure of the drilling operation with respect to the plurality of drilling parameters and the conditions of the plurality of drilling equipment, wherein the blackbox function is used as an objective function to represent the pre-determined performance measure of the drilling operation, and wherein the target value of the plurality of drilling parameters is determined by applying an iterative optimization algorithm to the objective function while meeting the user specified constraint.
 17. The wellsite according to claim 16, wherein the blackbox function comprises the non-linear relationship and at least one physics-based analytical relationship.
 18. The wellsite according to claim 17, the data gathering and analysis system further comprising functionality for: specifying, based on the blackbox function, the plurality of drilling parameters of a subsequent drilling operation.
 19. The wellsite according to claim 15, wherein the plurality of drilling parameters comprise a weight-on-bit value, a rotary speed value, and a pump flow rate value, and wherein the conditions of the plurality of drilling equipment comprise standpipe pressure, return flow rate, bit condition, hole learning index, equivalent circulating density (ECD), top-drive torque, top-drive hydraulics and electronics condition, stuck-pipe index, surface and downhole drill string vibration, bottomhole-assembly condition, drilling mud properties, and hole geometry.
 20. The wellsite according to claim 15, wherein the constraint defines an acceptable operating range of the conditions of the plurality of drilling equipment, and wherein the acceptable range comprises an extreme value of one or more of top drive torque, weight-on-bit, fluid flow rate, stick-slip index, bit wear rate, stuck pipe probability index, and cuttings concentration in annulus. 